Regularity of Milne Problem with Geometric Correction in 3D

TL;DR

This paper proves $W^{1, abla}$ regularity for solutions to the 3D Milne problem with geometric correction, enabling the validation of diffusive expansion in neutron transport with boundary conditions.

Contribution

It establishes new regularity results for the Milne problem with geometric correction in 3D, facilitating the diffusive expansion analysis.

Findings

Established $W^{1, abla}$ regularity for solutions.

Proved uniform $L^6$ estimates.

Validated diffusive expansion for neutron transport.

Abstract

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.